Proton spin relaxation in dilute methane gas: A symmetrized theory and its experimental verification

Abstract

Nuclear spin relaxation in low density methane gas is investigated theoretically and experimentally. A theory is developed in which full account is taken of the tetrahedral symmetry of the molecule. For a nuclear Larmor frequency of 30 MHz, the time evolution of the nonequilibrium magnetization is measured as a function of density between approximately 0.005 and 17 amagats at temperatures of 110, 150, and 295 K. In all cases, exponential relaxation is observed. By using the theory in conjunction with the known spin rotation constants and rotational energy levels of CH4, the measured values of the relaxation rate R1 have been fit very well at each temperature, both for the maximum value of R1 which contains no adjustable parameters and for the density dependence of R1 which contains a single parameter taken to be the collision cross section for molecular reorientation. The centrifugal distortion splittings of the rotational levels are shown to have an important influence on the observed values of R1 at 30 MHz and. more generally on the dependence of the time evolution of the nonequilibrium magnetization on density and frequency. On the basis of the theory, a new type of 'relaxation rate spectroscopy' is proposed. Non-exponential relaxation is predicted to occur at low densities when the nuclear Larmor frequency is tuned to a centrifugal distortion splitting.